Provide a short reasoning for each part

a. Determine whether following statements are true or false.

1. Regression through PRF provides best linear approximation for relationship between

two random variables x and y 2. Regression through PRF provides causal interpretation between two random variables x

and y

b. Determine whether this statement is true or false.

Larger variation in a regressor leads to smaller variance of OLS estimator for coefficient of that regressor.

c. Why asymptotic distribution of OLS estimators is a normal distribution? (in other words, which

theorem delivers the asymptotic normality?) Furthermore, what is the additional assumption that is needed to deliver normality for finite sample distribution of OLS estimators?